International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. B. ch. 3.4, pp. 385-397   | 1 | 2 |
https://doi.org/10.1107/97809553602060000562

Chapter 3.4. Accelerated convergence treatment of R−n lattice sums

D. E. Williamsa‡

aDepartment of Chemistry, University of Louisville, Louisville, Kentucky 40292, USA

References

First citation Arfken, G. (1970). Mathematical methods for physicists, 2nd ed. New York: Academic Press.Google Scholar
 First citation Bertaut, E. F. (1952). L'énergie électrostatique de réseaux ioniques. J. Phys. (Paris), 13, 499–505.Google Scholar
 First citation Bertaut, E. F. (1978). The equivalent charge concept and its application to the electrostatic energy of charges and multipoles. J. Phys. (Paris), 39, 1331–1348.Google Scholar
 First citation Busing, W. R. (1981). WMIN, a computer program to model molecules and crystals in terms of potential energy functions. Oak Ridge National Laboratory Report ORNL-5747. Oak Ridge, Tennessee 37830, USA.Google Scholar
 First citation Cummins, P. G., Dunmur, D. A., Munn, R. W. & Newham, R. J. (1976). Applications of the Ewald method. I. Calculation of multipole lattice sums. Acta Cryst. A32, 847–853.Google Scholar
 First citation Davis, P. J. (1972). Gamma function and related functions. Handbook of mathematical functions with formulas, graphs, and mathematical tables, edited by M. Abramowitz & I. A. Stegun, pp. 260–262. London, New York: John Wiley. [Reprint, with corrections of 1964 Natl Bur. Stand. publication.]Google Scholar
 First citation DeWette, F. W. & Schacher, G. E. (1964). Internal field in general dipole lattices. Phys. Rev. 137, A78–A91.Google Scholar
 First citation Evjen, H. M. (1932). The stability of certain heteropolar crystals. Phys. Rev. 39, 675–694.Google Scholar
 First citation Ewald, P. P. (1921). Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. (Leipzig), 64, 253–287.Google Scholar
 First citation Fortuin, C. M. (1977). Note on the calculation of electrostatic lattice potentials. Physica (Utrecht), 86A, 574–586.Google Scholar
 First citation Glasser, M. L. & Zucker, I. J. (1980). Lattice sums. Theor. Chem. Adv. Perspect. 5, 67–139.Google Scholar
 First citation Hastings, C. Jr (1955). Approximations for digital computers. New Jersey: Princeton University Press.Google Scholar
 First citation Madelung, E. (1918). Das elektrische Feld in Systemen von regelmässig angeordneten Punktladungen. Phys. Z. 19, 524–532.Google Scholar
 First citation Massidda, V. (1978). Electrostatic energy in ionic crystals by the planewise summation method. Physica (Utrecht), 95B, 317–334.Google Scholar
 First citation Nijboer, B. R. A. & DeWette, F. W. (1957). On the calculation of lattice sums. Physica (Utrecht), 23, 309–321.Google Scholar
 First citation Pietila, L.-O. & Rasmussen, K. (1984). A program for calculation of crystal conformations of flexible molecules using convergence acceleration. J. Comput. Chem. 5, 252–260.Google Scholar
 First citation Widder, D. V. (1961). Advanced calculus, 2nd ed. New York: Prentice-Hall.Google Scholar
 First citation Williams, D. E. (1971). Accelerated convergence of crystal lattice potential sums. Acta Cryst. A27, 452–455.Google Scholar
 First citation Williams, D. E. (1984). PCK83, a crystal molecular packing analysis program. Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington, Indiana 47405, USA.Google Scholar
 First citation Williams, D. E. (1989). Accelerated convergence treatment of [{\bi R}^{-n}] lattice sums. Crystallogr. Rev. 2, 3–23. Corrections: Crystallogr. Rev. 2, 163–166.Google Scholar